st: How much can we trust Stata's non-linear solver(s)?

at the weekend I read a paper by McCullough and Vinod on "Verifying the
solution from a nonlinear solver: A case study" in the June 2003 issue of
the American Economic Review. For those of you who are not in economics,
this is an absolute top-journal in our discipline, and the authors are
considered to be top-experts in the field. I was shocked (really, believe
me!) to learn how much can go wrong and goes wrong when one tries to find
the ML solution of such day-to-day problems as the parameters of a probit
model using a PC and several programs. The authors give examples, and they
argue that "the researcher's job is not done when the program reports
convergence - it is only beginning" (p. 876), and ask us to examine the
gradient, inspect the solution path, evaluate the Hessian, including an
eigensystem analysis, and profile the likelihood. Uff. Do I really have to
learn how to do all this? Do I have to use three or more different packages
to compare the solutions? Shall I demand this when I sit down to write my
next referee report later this week? Must I be aware that the next report I
receive will demand me to do all this?

Unfortunately, the authors do not name horses and riders (as we say in
Germany - in German, of course), so I have no idea whether Stata is among
the programs one can trust or not. Obviously, I want to know, and I am sure
many of the list-members share my view. Given that the acknowledgement
footnote of the paper mentions W. Gould, I hope he can tell us more.

From a slightly different perspective, would it be a good idea to
implement the steps suggested by the authors for a "post-convergence" check
in Stata ?

Given that I am no expert in numerical computing and all the related
difficulties, I would like to learn your opinions, experiences etc.